Equational reasoning with context-free families of string diagrams
Abstract
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.
Keywords
Cite
@article{arxiv.1504.02716,
title = {Equational reasoning with context-free families of string diagrams},
author = {Aleks Kissinger and Vladimir Zamdzhiev},
journal= {arXiv preprint arXiv:1504.02716},
year = {2015}
}
Comments
International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_9